U.S. Pat. Nos. 4,379,019 (Pool et al) and 5,037,501 (Lawson) describe hand held masking machines of the type adapted to apply strips of pressure sensitive adhesive coated masking tape from rolls of the tape carried on the masking machine along both edges of a sheet of masking material (e.g., paper or polymeric film) from a supply of masking material also carried on the masking machine. While these masking machines are usable for that purpose, they do not provide all of the flexibility that may be desired in the use of such a masking machine.